arXiv subjects

Saminthan Ponnusamy

Publications and source records attributed to Saminthan Ponnusamy.

3 recordsLinked to original sources

arXiv2024

Geometric subfamily of functions convex in some direction and Blaschke products

Consider the family of locally univalent analytic functions $h$ in the unit disk $|z|<1$ with the normalization $h(0)=0$, $h'(0)=1$ and satisfying the condition $${\real} \left( \frac{z h''(z)}{αh'(z)}\right) <\frac{1}{2} ~\mbox{ for $z\in \ID$,} $$ where $0<α\leq1$. The aim of this article is to show that this family has several elegant properties such as involving Blaschke products, Schwarzian derivative and univalent harmonic mappings.

math.CV↗

arXiv2019

Extreme points and support points of families of harmonic Bloch mappings

In this paper, the main aim is to discuss the existence of the extreme points and support points of families of harmonic Bloch mappings and little harmonic Bloch mappings. First, in terms of the Bloch unit-valued set, we prove a necessary condition for a harmonic Bloch mapping (resp. a little harmonic Bloch mapping) to be an extreme point of the unit ball of the normalized harmonic Bloch spaces (resp. the normalized little harmonic Bloch spaces) in the unit disk $\mathbb{D}$. Then we show that a harmonic Bloch mapping $f$ is a support point of the unit ball of the normalized harmonic Bloch spaces in $\mathbb{D}$ if and only if the Bloch unit-valued set of $f$ is not empty. We also give a characterization for the support points of the unit ball of the harmonic Bloch spaces in $\mathbb{D}$.

math.CV↗

arXiv2017

Lipschitz continuity of quasiconformal mappings and of the solutions to second order elliptic PDE with respect to the distance ratio metric

The main aim of this paper is to study the Lipschitz continuity of certain $(K, K')$-quasiconformal mappings with respect to the distance ratio metric, and the Lipschitz continuity of the solution of a quasilinear differential equation with respect to the distance ratio metric.

math.CV↗